Section 20.2-1

1. In this section you will: • Summarize the relationships between electric forces, charges, and distance. • Explain how to charge objects by conduction and induction. • Develop a model of how charged objects can attract a neutral object. • Apply Coulomb’s law to problems in one and two dimensions. Section 20.2-1

2. Electric Force Electric forces must be strong because they can easily produce accelerations larger than the acceleration caused by gravity. You also have learned that electric forces can be either repulsive or attractive, while gravitational forces always are attractive. Section 20.2-2

3. Electric Force Over the years, many scientists made attempts to measure electric forces. Daniel Bernoulli made some crude measurements in 1760. In the 1770s, Henry Cavendish showed that electric forces must obey an inverse square force law. Section 20.2-3

4. Forces on Charged Bodies The electrical forces you observed on tape strips also can be demonstrated by suspending a negatively charged, hard rubber rod so that it turns easily, as shown in the figure. Section 20.2-4

5. Forces on Charged Bodies If you bring another negatively charged rod near the suspended rod, the suspended rod will turn away. The negative charges on the rods repel each other. Section 20.2-5

6. Forces on Charged Bodies It is not necessary for the rods to make contact. The force, called the electric force, acts at a distance. If a positively charged glass rod is suspended and a similarly charged glass rod is brought close, the two positively charged rods also will repel each other. Section 20.2-6

7. Forces on Charged Bodies If a negatively charged rod is brought near a positively charged rod, however, the two will attract each other, and the suspended rod will turn toward the oppositely charged rod. Section 20.2-7

8. Forces on Charged Bodies The results of your tape experiments and these actions of charged rods can be summarized in the following way: • There are two kinds of electric charges: positive and negative. • Charges exert forces on other charges at a distance. • The force is stronger when the charges are closer together. • Like charges repel; opposite charges attract. Section 20.2-8

9. Forces on Charged Bodies Neither a strip of tape nor a large rod that is hanging in open air is a very sensitive or convenient way of determining charge. Instead, a device called an electroscope is used. Section 20.2-9

10. Forces on Charged Bodies An electroscope consists of a metal knob connected by a metal stem to two thin, lightweight pieces of metal foil, called leaves. The figure on the right shows a neutral electroscope. Note that the leaves hang loosely and are enclosed to eliminate stray air currents. Section 20.2-10

11. Forces on Charged Bodies When a negatively charged rod is touched to the knob of an electroscope, electrons are added to the knob. These charges spread over all the metal surfaces. As shown in the figure, the two leaves are charged negatively and repel each other; therefore, they spread apart. Section 20.2-11

12. Forces on Charged Bodies The electroscope has been given a net charge. Charging a neutral body by touching it with a charged body is called charging by conduction. Section 20.2-12

13. Forces on Charged Bodies The type of charge carried by an electroscope can be determined by observing the leaves when a rod of known charge is brought close to the knob. The leaves will spread farther apart if the rod and the electroscope have the same charge. The leaves will fall slightly if the electroscope’s charge is opposite that of the rod. Section 20.2-13

14. Forces on Charged Bodies Suppose you move your finger, or any uncharged object, close to a positively charged object. The negative charges in your finger will be attracted to the positively charged object, and the positive charges in your finger will be repelled. Your finger will remain neutral, but the positive and negative charges will be separated. Section 20.2-14

15. Forces on Charged Bodies The electric force is stronger for charges that are closer together; therefore, the separation results in an attractive force between your finger and the charged object. The force that a charged ruler exerts on neutral pieces of paper is the result of the same process, the separation of charges. The negative charges at the bottom of thunderclouds also can cause charge separation in Earth. Section 20.2-15

16. Charging by Induction Section 20.2-16

17. Forces on Charged Bodies Grounding can also be used as a source of electrons. If a positive rod is brought near the knob of a grounded electroscope, electrons will be attracted from the ground, and the electroscope will obtain a negative charge. When this process is employed, the charge induced on the electroscope is opposite of the object used to charge it. Because the rod never touches the electroscope, its charge is not transferred, and it can be used many times to charge objects by induction. Section 20.2-17

18. Coulomb’s Law Section 20.2-18

19. Coulomb’s Law The amount of charge that an object has is difficult to measure directly. Coulomb’s experiments, however, showed that the quantity of charge could be related to force. Thus, Coulomb could define a standard quantity of charge in terms of the amount of force that it produces. The SI standard unit of charge is called the coulomb (C). Section 20.2-19

20. Coulomb’s Law One coulomb is the charge of 6.24×1018 electrons or protons. The charge on a single electron is 1.60×10−19 C. The magnitude of the charge of an electron is called the elementary charge. Section 20.2-20

21. Coulomb’s Law Even small pieces of matter, such as coins, contain up to 106 C of negative charge. This enormous amount of negative charge produces almost no external effects because it is balanced by an equal amount of positive charge. If the charge is unbalanced, even as small a charge as 10−9 C can result in large forces. Section 20.2-21

22. Coulomb’s Law Coulomb’s Law According to Coulomb’s law, the magnitude of the force on charge qA caused by charge qB a distance r away can be written as follows: Section 20.2-22

23. Coulomb’s Law The force between two charges is equal to Coulomb’s constant, times the product of the two charges, divided by the square of the distance between them. The Coulomb’s law equation gives the magnitude of the force that charge qA exerts on qB and also the force that qB exerts on qA. These two forces are equal in magnitude but opposite in direction. Section 20.2-23

24. Coulomb’s Law The electric force, like all other forces, is a vector quantity. Force vectors need both a magnitude and a direction. However, the Coulomb’s law equation gives only the magnitude of the force. To determine the direction, you need to draw a diagram and interpret charge relations carefully. Section 20.2-24

25. Coulomb’s Law If two positively charged objects, A and B, are brought near each other, the forces they exert on each other are repulsive. If, instead, B is negatively charged, the forces are attractive. Section 20.2-25

26. Coulomb’s Law in Two Dimensions Sphere A, with a charge of +6.0 µC, is located near another charged sphere, B. Sphere B has a charge of −3.0 µC and is located 4.0 cm to the right of A. a. What is the force of sphere B on sphere A? b. A third sphere, C, with a +1.5-µC charge, is added to the configuration. If it is located 3.0 cm directly beneath A, what is the new net force on sphere A? Section 20.2-26

27. Coulomb’s Law in Two Dimensions Step 1: Analyze and Sketch the Problem Section 20.2-27

28. Coulomb’s Law in Two Dimensions Establish coordinate axes and sketch the spheres. Section 20.2-28

29. Coulomb’s Law in Two Dimensions Show and label the distances between the spheres. Section 20.2-29

30. Coulomb’s Law in Two Dimensions Diagram and label the force vectors. Section 20.2-30

31. Coulomb’s Law in Two Dimensions Identify the known and unknown variables. Known: qA = +6.0 µC qB = −3.0 µC qC = +1.5µC rAB = 4.0 cm rAC = 3.0 cm Unknown: FB on A = ? FC on A = ? Fnet = ? Section 20.2-31

32. Coulomb’s Law in Two Dimensions Step 2: Solve for the Unknown Section 20.2-32

33. Coulomb’s Law in Two Dimensions Find the force of sphere B on sphere A. Section 20.2-33

34. Coulomb’s Law in Two Dimensions Substitute qA = 6.0 μC, qB = 3.0 μC, rAB = 4.0 cm Because spheres A and B have unlike charges, the force of B on A is to the right. Section 20.2-34

35. Coulomb’s Law in Two Dimensions Find the force of sphere C on sphere A. Section 20.2-35

36. Coulomb’s Law in Two Dimensions Substitute qA = 6.0 µC, qC = 1.5 µC, rAC = 3.0 cm Spheres A and C have like charges, which repel. The force of C on A is upward. Section 20.2-36

37. Coulomb’s Law in Two Dimensions Find the vector sum of FB on A and FC on A to find Fnet on sphere A. Section 20.2-37

38. Coulomb’s Law in Two Dimensions Substitute FB on A = 1.0×102 N, FC on A = 9.0×101 N Section 20.2-38

39. Coulomb’s Law in Two Dimensions Substitute FC on A = 9.0×101 N, FB on A = 1.0×102 N Section 20.2-39

40. Coulomb’s Law in Two Dimensions Step 3: Evaluate the Answer Section 20.2-40

41. Coulomb’s Law in Two Dimensions Are the units correct? (N·m2/C2)(C)(C)/m2 = N. The units work out to be newtons. Does the direction make sense? Like charges repel; unlike charges attract. Is the magnitude realistic? The magnitude of the net force is in agreement with the magnitudes of the component forces. Section 20.2-41

42. Coulomb’s Law in Two Dimensions Step 1: Analyze and Sketch the Problem Establish coordinate axes and sketch the spheres. Show and label the distances between the spheres. Diagram and label the force vectors. The steps covered were: Section 20.2-42

43. Coulomb’s Law in Two Dimensions Step 2: Solve for the Unknown Find the force of sphere B on sphere A. Find the force of sphere C on sphere A. Step 3: Evaluate the Answer The steps covered were: Section 20.2-43

44. Coulomb’s Law Coulomb’s law is valid only for point charges or uniform spherical charge distributions. That is, a charged sphere may be treated as if all the charge were located at its center, if the charge is spread evenly across its entire surface or throughout its volume. Therefore, it is important to consider how large and how far apart two charged spheres are before applying Coulomb’s law. When shapes such as long wires or flat plates are considered, Coulomb’s law must be modified to account for the nonpoint charge distributions. Section 20.2-44

45. Application of Electrostatic Forces There are many applications of electric forces on particles. For example, these forces can collect soot in smokestacks, thereby reducing air pollution, as shown in the figure. Section 20.2-45

46. Application of Electrostatic Forces Tiny paint droplets, charged by induction, can be used to paint automobiles and other objects very uniformly. Photocopy machines use static electricity to place black toner on a page so that a precise reproduction of the original document is made. Section 20.2-46

47. Application of Electrostatic Forces In other instances, applications are concerned with the control of static charge. For example, static charge can ruin film if it attracts dust, and electronic equipment can be damaged by the discharge of static charge. In these cases, applications are designed to avoid the buildup of static charge and to safely eliminate any charge that does build up. Section 20.2-46

48. Question 1 What will happen if a positively charged rod is suspended freely in air and another positively charged rod is brought near the suspended rod? Section 20.2-47

49. Question 1 A. The more you bring the rod closer to the suspended rod, the more it will attract. B. The more you bring the rod closer to the suspended rod, the less it will attract. C. The more you bring the rod closer to the suspended rod, the more it will repel. D. The more you bring the rod closer to the suspended rod, the less it will repel. Section 20.2-47

50. Answer 1 Reason:Electric forces depend on the charge and the distance between the two materials. This is summarized on the next slide. Section 20.2-48